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No doubt reliable electroencephalogram (EEG) analysis methods capable of predicting the epileptic seizures would be of great value. This paper presents a new approach, based on bispectrum analysis of EEGs and artificial neural network(ANN), which predicts seizures in seven patients with epilepsy. Eight channels of EEG were collected in each subject in Epilepsy Center of Xijing Hospital. The maximum magnitude and the weighted center of EEG bispectrum (WCOB) were extracted from the EEG bispectrum contour and a four layer(24-10-2-1) ANN was employed for prediction. Training and testing the ANN used the 'leave one out' method. The proposed system was able to correctly predict the succedent seizures and prediction times are from 12 to 24 seconds, prior to the onset of epileptic seizures.